 | Robert Potts - Geometry - 1876 - 446 pages
...less, that is, ' when the greater contains the less a certain number of times exactly.' m. " Ratio is a mutual relation of two magnitudes of the same kind to one another, in respect of quantity." IV. Magnitudes are said to have a ratio to one another, when the less can be multiplied so as to exceed... | |
 | George Elliot Voyle, G. de Saint-Clair-Stevenson - English language - 1876 - 676 pages
...property under their charge, if committed through carelessness, &c. Batió — In mathematics, the mutual relation of two magnitudes of the same kind to one another, in respect of quantity. Ratios are divided into arithmetical and geometrical. An arithmetical ratio consists in the difference... | |
 | Āryabhaṭa - 1878 - 100 pages
...the less, that ia, when the greater contains the less a certain number of times exactly. XXIX. The mutual relation of two magnitudes of the same kind to one another, in respect of quantity, is called their ratio. XXX. The first of four magnitudes is said to have the same ratio to the second,... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...by the less; that is, when the greater contains the less a certain number of times exactly. 3. Ratio is a mutual relation of two magnitudes of the same...ratio to one another, when the less can be multiplied go as to exceed the other. 5. The first of four magnitudes is said to hare the same ratio to the second,... | |
 | Euclides - Euclid's Elements - 1881 - 236 pages
...expressed, like many others, in commensurate terms; for their common measure, or common unit is unknown. IV. Magnitudes are said to have a ratio to one another, when the less can he multiplied so as to exceed the other. This definition is intended as a test of the likeness or similarity... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...by the less; that is, when the greater contains the less a certain number of times exactly. 3. Ratio is a mutual relation of two magnitudes of the same...exceed the other. 5. The first of four magnitudes is said to have the same ratio to the second, that the third has to the fourth, when any equimultiples... | |
 | Leonard Marshall - 1883 - 184 pages
...circumference of each wheel? V.— RATIO, PROPORTION, AND VARIATION. 1. Ratio is defined by Euclid as the mutual relation of two magnitudes of the same kind to one another in respect of quantity (see Bk. V. Def. iii.). In Algebra the ratio of a : b is measured by the . , .. antecedent aj ., .... | |
 | Alexander Mackenzie - 1884 - 776 pages
...established between things which are not of the same kind. Euclid's definition is as follows : — " Ratio is a mutual relation of two magnitudes of the same kind to one another in respect of quantity." " Magnitudes which have the same ratio are called proportionals. When four magnitudes are proportionals... | |
 | Alexander Mackenzie, Alexander Macgregor, Alexander Macbain - Clans - 1884 - 604 pages
...established between things which are not of the same kind. Euclid's definition is as follows:—" Ratio is a mutual relation of two magnitudes of the same kind to one another in respect of quantity." " Magnitudes which have the same ratio are called proportionals. When four magnitudes are proportionals... | |
 | Euclides - 1884 - 434 pages
...are multiples that contain these magnitudes, respectively, the same number of times. 4. Ratio is a relation of two magnitudes of the same kind to one another, in respect of quantuplicity (a word which refers to the number of times or parts of a time that the one is contained... | |
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A greater magnitude is said to be a multiple of a less, when the greater is measured by the less ; that is, ' when the greater contains the less a certain number of times exactly.' 3. ' Ratio is a mutual relation of two magnitudes of the same kind to... 
